Method and apparatus for designing photomasks

ABSTRACT

Method and apparatus for designing the photomask in the course of designing the Levenson-type phase shift mask, capable of automatically arranging the shifter, of not causing a contradictory spot in a circuit designing stage and of automatically forming a final layout achieving maximum integrity. The method includes the steps of: forming symbolic layout data in which a distance between adjacent clear areas is set to an arbitrary value; determining regions having a mutual phase difference 0° or 180° of light transmitting through adjacent patterns corresponding to the clear areas in the symbolic layout data; executing compaction of the symbolic layout in a manner that design rule S1 is adopted to the clear areas neighboring with the phase difference of 180° and design rule S2 is adopted to the clear areas neighboring with the phase difference of 0°; and forming mask layout data such that S1 is less than S2.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates to method and apparatus for designing aphotomask for use with production of a semiconductor device, and itparticularly relates to the method and apparatus for designing aphase-shifting mask which is suitable for projecting a miniaturizedpattern for the semiconductor device production.

2. Background Art

A photomask on which an original mask pattern of a VLSI is drawn isirradiated by an incident ray which is partially coherent. The photomaskwill be simply referred to as a mask hereinafter. Patterns on the maskare projected on to a semiconductor wafer so as to execute photolithography. For a projection lithography system realizing thephotolithography system, there is required a further miniaturizedpattern to be copied on to the wafer.

The minimum feature size of the pattern fabricated is expressed by adegree of resolution therefor. The resolution is evaluated by howaccurately two adjacent exposed regions on a resist coated semiconductorsubstrate can be separated without being overlapped, by utilizing, say,a mask pattern whose light transmissive regions and light shieldingregions; are periodically changed. In order to improve the minimumresolution, there is known a method where phase difference is given tothe incident ray which passes a pair of adjacent light transmissiveregions on the mask.

As for the method where the phase difference is given to the incidentray which passes a pair of adjacent light transmissive regions on themask, such a method is conventionally known and discussed in a paperentitled "Improving Resolution in Photolithography with a Phase-ShiftingMask" written by Mark D. Levenson et al. (IEEE Transaction on ElectronDevices, Vol ED-29 No. 12, 1982, page 1828).

FIG. 2 shows a Levenson type phase shifting mask suggested by the abovepaper. In the same figure, on mask substrate 14 there are formed aplurality of light-shielding (opaque) regions 16 and light transmissiveregions serving as the original images for the patterns and there isprovided phase shifter 15 which supplies a phase difference between theincident rays passing through the clear region. The phase shifter 15 ismade of transparent material against the incident rays. Phase shifter 15is arranged to be disposed on either side of a pair of the adjacentlight transmissive regions. The phase shifter 15 may be simply referredto as a shifter hereinafter.

The shifter needs to satisfy a condition of

    d=λ/{2(n-1)},

where d is film thickness of the shifter, n an index of refraction and λa wavelength of the incident ray. There is a phase difference betweenthe ray which passed through the shifter and other transmission raysthat didn't pass through the shifter, so that light intensity of the raya pattern boundary under a light shielding region on the semiconductorsubstrate becomes near zero. As a result thereof, adjacent regions areseparated, thus improving the resolution therefor.

In connection with the paper discussing the Levenson type phase shiftingmask and an automatic designing apparatus therefor, there is a paperentitled "Automatic Pattern Generation System for Phase Shifting Mask"authored by Noboru Nomura et al. (Symposium on VLSI Technology, JSAPCATNo.AP911210, pp. 95-96, Oiso, Japan, May. 1991). Nomura et al'stechnique will be referred to as a first conventional art hereinafter.In Nomura et al's paper, a dynamic random access memory (DRAM) isdesigned by making use of the apparatus for automatically designing theLevenson type phase shifting masks. In the event that the phase of lightrays passing through the pattern contained in input layout areautomatically determined, firstly an other arbitrary (or the phase-to-bedetermined) pattern is selected so that its phase is set to 0°.Thereafter, the phase of arbitrary pattern is set opposite to the phaseof pattern facing to the phase-to-be-determined pattern which has a sidelongest, among patterns whose phases are already determined; when thereexist a plurality of patterns facing the longest sides to thephase-to-be determined pattern, a system of Nomura et al. gives warningand aborts a processing.

Moreover, as a second conventional art, there is another paper entitled"Investigating Phase-shifting Mask Layout Issues Using a CAD Toolkit"written by Andrew R. Neureuther et al. (IEDM Technical Digest,pp705-708, 1991). This paper discusses about an automatic designingsystem where a circuit designer determines a shrink factor for inputlayout, the phases of the light rays passing through the pattern in thelayout are automatically assigned against the shrank pattern, and, ifthere is a portion where the phase assignments conflict, such portion isnotified to the designer.

Moreover, as a third conventional art, there is still another paperentitled An Automatic Shifter Pattern Generator for Levenson-type PSMS(1) written by Kazuko Ooi et al. Extended Abstracts of the 53 rd AutumnMeeting 1992: The Japan society of Applied Physics No.2 p478, lectureno.16P-L-11). In this third conventional art, when the spacing betweenthe light transmissive regions contained in input layout is less than athreshold value, opposite phases are assigned to the pair of the lighttransmissive regions, and when there exists a conflict spot during thephase assignment, such a spot is notified to the designer. 0oi et aldiscusses such a method and apparatus which has functions of a phaseassignment and a verification against a partially phase assigned layout.

Moreover, as a fourth conventional art, there is still another paperentitled "Algorithm for Phase Shift Mask Design with Priority on ShifterPlacement" written by Akemi Moniwa et al. (Digest of PapersMicroprocess, '93, pp50-51, 1993). In this paper discussing the phaseassignment method, firstly pairs of adjacent light transmissive regions(or apertures) having spacings less than a threshold value are made.These pairs are given weightings, respectively and starting from a pairhaving heavier weighting factors, the mutual phases are determined to beopposite, so that the conflict spots will occur in a pair having lighterweighting factors.

In the above described first, third and fourth conventional arts, phasesare assigned in the geometrically fixed layout. Thus, whether or notthere exists a conflict spot in the layout is determined already at astage of making the layout. For example, referring to FIG. 1, it isimpossible to arrange shifters without causing a conflict spot. Forinstance, in the first conventional art, arrangement will be properuntil phase 0° is given to light transmissive region (pattern) 11 andthen phase 180° is given to light transmissive region (pattern) 12.However, when a phase is assigned to light transmissive region 13,contradiction will be caused. This is because the light transmissiveregion 13 is facing to transmissive region 12 in the upper portionindicated by x and facing to transmissive region 11 in the lower portionindicated by y in FIG. 1, and; delete "clear" and insert lighttransmissive the lengths of side facing with the clear region 13 andclear region 11 are same, and because phase of light transmissive region11 differs from that of light transmissive region 12, so that a properphase can not be assigned to the light transmissive region 13, thuscausing the contradiction. Even if the order of assigning the phases ischanged, it is not possible to arrange the shifter without causing thecontradiction.

Moreover, in the third conventional art referring to FIG. 1, when phase0° is assigned to the light transmission region 11 and phase 180° isassigned to both the light transmissive regions 12 and 13 which areneighboring to the light transmissive region 11 having spacing thethreshold, the same phase is assigned to both the light transmissiveregions 12 and 13 each of which is neighboring to the other within thethreshold spacing, thus causing contradiction. In other words, referringto the light transmissive regions 11 and 13, they are adjacent to eachother within the threshold (←→) in a lower region indicated with y inFIG. 1.

Similarly, in the fourth conventional art, the light transmissiveregions disposed adjacent to each other need to have opposite phases toeach other. Thus, it is impossible to arrange shifters without causing aconflict spot in the layout shown in FIG. 1. In these layouts havingcontradictory spots (conflict spots), the circuit designer will berequired to modify the layout until he/she could eliminate such conflictspots. Since the circuit designer will spend much time in modifying suchconflict spots manually, such manual operation is very inefficient.

Moreover, in the second conventional art, a whole layout is scaled downby providing the input layout with certain uniform shrink factor. Thus,the number-of conflict spots will increase as the scale-down operationproceeds. In this second conventional art too, the circuit designer isrequired to modify the layout about presented conflict spots.

As described above, when the phases are assigned after the layout iscompleted in the course of designing the Levenson-type phase shiftingmask, there often exist conflict spots in the layout. Thus, the designerneeds to engage himself/herself in modifying the conflict spots, thusdeteriorating designing efficiency. This drawback is a major problem inapplication of the Levenson-type phase shifting mask.

SUMMARY OF THE INVENTION

In view of the foregoing drawbacks, it is therefore an object of thepresent invention to provide method and apparatus for designing thephotomask in the course of designing the Levenson-type phase shift mask,which are capable of automatically assigning the phase, without causinga contradictory spot in a circuit designing stage, and automaticallyforming a final layout achieving maximum; integration density, so as toimprove the designing efficiency significantly.

According to the present invention, there is provided a method fordesigning a phase shifting mask, comprising the steps of: formingsymbolic layout data in which a spacing between adjacent lighttransmissive areas is set to an arbitrary value; assigning oppositephase (0° or 180° ) to the pairs of adjacent light transmissive regionsin the symbolic layout data; executing compaction of the symbolic layoutin a manner that minimum spacing (or design rule) S1 is adopted to thepairs of adjacent light transmissive regions which have the phasedifference of 180° and minimum spacing (or design rule) S2 is adopted tothe pairs of adjacent light transmissive regions which have the phasedifference of 0°; and forming mask layout data such that S1 is less thanS2.

There is also provided apparatus for designing a phase shifting mask,which comprises: means for forming symbolic layout data; means forexecuting first compaction on a phase-shift applied layer by design rulethat is an arbitrary value; means for assigning phases (either 0° or180° ) to nets composed of electrically equivalent elements in thecompaction-executed phase-shift applying layer; and means for executingsecond compaction in a manner that design rule S2 is adopted to a pairsof nets having same phase and design rule S1 is adopted to a pairs ofnets having opposite phase, where spacing S1 is less than S2.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features and advantages of the presentinvention will become more apparent from the following description ofthe preferred embodiment taken in conjunction with the accompanyingdrawings, in which:

FIG. 1 shows an exemplary pattern layout for explaining conventionalpractices.

FIG. 2 shows a phase shifter 15 in relation to a light-shielding region16 and a mask substrate 14.

FIG. 3 shows a flowchart of phase assignment technique according to thebasic idea of the present invention.

FIG. 4A shows a result where the phases are assigned in the layout whereadjacent patterns are designed in terms of minimum distance of S3.

FIG. 4B shows a result where the layout of FIG. 4A iscompaction-executed.

FIG. 5A shows a result where the phases are assigned in the layout wherethe patterns are designed in terms of minimum distance S3.

FIG. 5B shows a result where the layout of FIG. 5A iscompaction-executed.

FIG. 6 shows procedures for the compaction.

FIG. 7 shows a flowchart of phase assignment technique according to thefirst embodiment of the present invention.

FIGS. 8A-8D show four different results of layouts obtained after thecompaction is executed on four types of phase assignment results.

FIG. 9 illustrates the second embodiment of the present invention.

FIGS. 10(a) through 10(d) show contact patterns according to the secondembodiment.

FIG. 11 illustrates an example when the second embodiment is applied.

FIG. 12 illustrates apparatus for automatic phase assignment accordingto the first embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Features of the present invention will become apparent in the course ofthe following description of exemplary embodiments which are given forillustration of the invention and are not intended to be limitingthereof. Embodiments of the present invention will now be described withreference to the drawings.

In a designing apparatus for realizing the following embodiments, theremay be utilized an ordinary computer equipped with a CPU which executesvarious processings, an input system such as a keyboard, a mouse, alight pen, and an external system such as a memory unit and disk unit,and an output system such as a display, printer. In this case, anarithmetic processing and so on are executed in an processing portion inthe CPU, and storage of each datum is performed in the memory unit andexternal system in the CPU.

BASIC IDEA

FIG. 3 shows a flowchart for assigning phases to light transmissive (orclear) regions according to a basic method for the present invention.Referring to FIG. 3, layout data are made so that a minimum spacingbetween neighboring patterns (that is, between adjacent lighttransmissive regions) is an arbitrary spacing S3 as shown in STEP 1.Step 1 may be carried out manually by a circuit designer, or may beperformed by an automatic designing software utilizing the abovedescribed computer. Possibly, a symbolic layout which ignores a designrule minimum linewidth and minimum spacing can be formal first, and thenthe compaction can be executed on the thus-formed symbolic layout sothat the minimum spacing between the neighboring patterns is S3.

In general, a symbolic layout is a schematic layout diagram described byonly utilizing relative positions of circuit comprising elements such asa transistor, contact and wire. In other words, the symbolic layout is adimensionless layout in which only relative positions between symbolsare specified; the symbols may be wire, transistor, contact and so on.Compaction is defined to be that the schematic layout diagram (symboliclayout) is automatically converted to a final mask pattern in accordancewith a design rule. A tool used therefor is called a compactor. In otherwords, the symbolic layout converted into a final mask layout bycompactor software which minimizes the mask area, fulfilling designrules at the same time.

Some of exemplary ways for determining the (step 2) will be describedbelow.

First Example

The minimum spacing between patterns in the layout is measured. Thenpairs of neighboring patterns having the minimum spacing of S3 ismemorized. Tracing thus memorized neighboring relationship, the phase isassigned in a manner that a pair of neighboring patterns are assignedopposite phases to each other; Then, when there exists a contradictoryspot or conflict spot, phase assignment procedure is continued while thecontradictory spot is left as such. Here, the contradictory or conflictspot indicates a spot where the neighboring patterns have the same phaseto each other.

As an applied example for this first example, the phases may be assignedin the following manner. The designer assigns phases specifically in animportant region in the layout. Referring to FIG. 4A, suppose that theregion A enclosed by a rectangle in an upper portion of the layout isimportant one. Therefore, the phases are assigned 0° and 180°alternately.

Second Example

Spacings between the patterns in input layout data are measured. Then,among the pairs of patterns which are neighboring to each other withinthe spacing of S3, a priority is given to a pair of patterns where thelength of sides facing less than S3 is longer, so that the pair of thepatterns is assigned opposite phase to each other (see FIG. 5A).Referring to FIG. 5A, the phases are assigned opposite to each other inthe order of the pair of patterns 4-5, 2-3, 1-2, 3-4, 3-6, 6-4. As aresult thereof, a pair of patterns 6-4 bears a contradictory spot.

Third Example

Here, as a phase assigning technique, neighboring relationship ofpatterns is obtained from the relation whether or not the minimumspacing between the patterns in the mask layout is less than a thresholdvalue. It is possible that the neighboring relationship is expressed bya graph where each line segment thereof is weighted. (Here, theneighboring relationship is expressed as the graph in which each patternis represented by a node and neighboring patterns are connected by aline segment.) Then, the lights transmitting through the patternscorresponding to nodes on a single line segment are assigned oppositephases, starting from a line segment having a greater weighting. Thenthe conflict spots may appear on smaller weighted line segments.

Furthermore, as conditions for the weighting of the line segments forabove-said graph, at least one of the following weighting techniques, orcombination thereof may be adopted:

(1) Greater weighting is given for less minimum spacing betweenpatterns;

(2) Greater weighting is given for a shorter side of patterns facingeach other within the threshold;

(3) Heavier weighting is given to a side of the graph included ingreater number of closed loops;

(4) Greater weighting is given for pattern regions having less areawithin the threshold; and

(5) Weighting is given at discretion of the circuit designer.

In other words, after pairs of patterns adjacent within the thresholdare made, the weighting is given to each pair of the patterns. Then, inthe order of the pair of patterns having less weighting factor towardheavier weighting factor, the opposite phases are assigned; heavierweighting patterns can be modified more easily. Even though the spotshaving the same phase might be caused thereby, they will bring almost nodeterimental affect.

After the phases are assigned as described above, the layout is shrunkas much as possible by utilizing a conventionally available programcalled a compactor (STEP 3 in FIG. 3). The compactor is a kind ofcomputer-aided design (CAD) software, and has function of contractingarea of the input layout as much as possible while satisfying variousconstraints or conditions. Moreover, a usual compactor can performcompaction so that consistency between plural layers can be kept.However, the usual compactor accepts the symbolic layout as an input.Therefore, there may be a case where the layout thus formed above needbe input to the compactor after it is translated into the symboliclayout.

Referring to FIG. 6, a pair of patterns having opposite phase to eachother is given condition of the minimum spacing being S1, while the pairhaving same phase is given condition of the minimum spacing D2 for thecompactor. The inter-pattern spacing S1 and S2 are the minimum spacings(design rule) of patterns where line and space patterns are resolvablewhen the pattern-transmitting lights are of opposite phases, and of thesame phases drawn, respectively. Naturally, S2 is greater than S1 (S1<S2). Though S3 can be any arbitrary value, suppose that S3 is equal orgreater than S2. In this embodiment, though not specifically defined inthis specification, a minimum line width of pattern itself is generallydetermined in advance in the course of circuit designing. Moreover, inthe layout, there generally exist various layers in addition to aphase-shift applied layer and a phase-shift-pattern output layer. A mostsuitable design rule will be applied to each layer for its compaction.

Referring still to FIG. 6, a group of patterns to which 0° is assignedas a result of phase assignment, is moved to layer 1, while a group ofpatterns of 180° is moved to layer 2. Thereafter, pairs of patterns onthe same layer are separated by more than S2, and other pairs ofpatterns belonging to different layers are separated by more than S1.When the compaction is executed with the above condition, there areformed layer 1' and layer 2' shown in FIG. 6. Thereafter, synthesizingthese layers, there is formed layer 0'. The layer 0' represents aphase-shift applied layer, and either blank patterns or hatched patternscorrespond to the phase-shift pattern.

The results of compaction executed omitting other. layers and using onlythe condition of S1 for the pair of patterns having opposite phases andS2 for the pair of patterns having the same phases are shown in FIG. 4Band FIG. 5B, respectively. In these examples, the compaction wasexecuted only in X direction, since no pattern is arranged in the Ydirection. Here, the X direction indicates the direction vertical to thelines in figures, and the Y direction indicates the direction along thelines.

First Embodiment

FIG. 7 is a flow chart showing procedure for designing phase shift masksaccording to a first embodiment based on the basic idea.

Referring to FIG. 7, firstly, symbolic layout data are prepared (STEP1). The symbolic layout data may be manually formed by the circuitdesigner, or may be made by utilizing an automatic designing software.It is also possible that the data are made by converting theconventionally available mask layout to the symbolic layout.

Thereafter, the compaction is executed on the phase-shift applied layerby the design rule S3 (STEP 2). As for layers other than the phase-shiftapplied layer, each appropriate design rule therefor shall be utilized.Thereby, the design rules are fulfilled and the conversion process isperformed so that the mask area, or the chip size is minimized.

An output of the above compaction will be either the compaction-executed(or compacted) symbolic layout or the mask layout. Regardless of thelayout, the phase of the light transmitting against a net in the layoutis determined (STEP 3 in FIG. 7). In other words, it is determined towhich light transmissive region in the layout a phase of 180° is to beassigned, and to which light transmissive region phase of 0° is to beassigned.

In this phase assignment, the opposite phase will be assigned as much aspossible when the minimum spacing between nets is S3. In the case of thecompaction-executed symbolic layout, the net indicates collection ofelectrically equivalent elements, while the net indicates a continuouslight transmissive region on the mask in a case of the mask layout.

Specifically speaking, the phase will be assigned in the followingmanner.

The minimum spacing between the nets of the symbolic layout or masklayout is measured. The opposite phase is assigned as much as possibleto a pair of nets whose spacing is S3. To a pair of the nets whosespacing is greater than S3, the same or opposite phase will be assigned.

After the phases are assigned as described above, the layout iscompaction-executed as much as possible by utilizing again thecompactor's program (STEP 4 in FIG. 7). Then, as for the phase-shiftapplied layers, there are utilized conditions which include design ruleS2 between the same phase nets, and design rule S1 between the oppositephase nets. Here, S1 indicates a resolution limit spacing for a pair ofopenings having the opposite phases on the mask, or a somewhat greaterthan the resolution limit spacing. S2 indicates another resolution limitspacing for a pair of openings having the same phase on the mask, or asomewhat greater than the resolution limit spacing. Though the magnitudeof S3 may be arbitrary, it is preferably greater than S2. Here, thevalues of S1, S2 and S3 are those corresponding to the practical minimumspacings of patterns on a semiconductor chip

When there are plural types of phase assignment results in STEP 3 inFIG. 7, the compaction is executed on to each phase assignment result(STEP 3), and then a layout whose mask area is minimum is selected. Forexample, FIGS. 8A-8D show four different results of layouts obtainedafter the compaction is executed on four types of phase assignmentmethods. Among FIGS. 8A-8D, the area occupied by the layout is minimumin the phase assignment method of FIG. 8C. In this case, the layoutrepresented by FIG. 8C is selected.

Next, STEP 4 in FIG. 7 will be described in detail. The net to which thephase of 180° is assigned in the symbolic layout is moved to aphase-shift-pattern output layer. Here, the symbolic layout, the patternis not defined directly in the layer. Rather, the pattern is definedtemporarily in the symbols, and the symbols are defined in the symboliclayout. Therefore, the pattern can not be moved directly from thephase-shift applied layer to the phase-shift-pattern output layer.Instead, some symbols are replaced by its derivative symbols. A methodtherefor will be described below referring to FIG. 9-FIG. 11.

Second Embodiment

Referring to FIG. 9, suppose that the phase-shift applied layers are thefirst aluminum and the second aluminum. Assume that, as a result ofphase assignments in each layer, the phases of 180° are assigned to thefirst aluminum's patterns which are included in symbols 22, 24, 30, 32and the second aluminum's patterns included in symbols 26, 27, 30, 31,respectively. Then, since each wiring includes only a single layer ofthe phase-shift applied layer in symbols, it suffices that the symbols22, 24, 26, 27 are simply replaced with symbols 35, 36, 37, 38 using thephase-shift-pattern-output layer (FIG. 11).

Symbols 29, 30, 31, 32 are contacts between the first and secondaluminum wirings, and specific patterns for these symbols are expressedin FIG. 10(a). In FIG. 10(a), the first aluminum wiring pattern A andthe second aluminum wiring pattern B are of square shape 34, and contactportion 33 is of square shape 33 which is smaller than the shape 34.Accordingly, the symbol for the contact includes two-phase-shift appliedlayers, and thus four types of derivative symbols need be formed asshown in FIG. 10(a), FIG. 10(b), FIG. 10(c) and FIG. 10(d). Utilizingthese four types of symbols, contacts 30-32 in FIG. 9 are replaced bycontacts 39-41. For example, contact 31 should consist of a contactbetween the first aluminum wiring and the second aluminum phase shiftwiring, so that it is replaced by contact 2 shown in FIG. 10(c).

Namely, in a case where each symbol includes n of phase-shift appliedlayers (where n indicates an integer greater than one), it will berequired to form 2^(n) types of derivative symbols in combination of thephase-shift applicable layer and its phase-shift-pattern output layer.That is, when n is two, there will be required four different types ofcontacts. Though the wiring and the contact were used as an example forsymbol here, the situation will be the same when other symbol such astransistor is used. Moreover, though described above is the symbolincluding one or two layers of phase-shift applicable layer, the casewith more than three layers is similar thereto.

By the above-described technique, after patterns having phase of 180° inthe phase-shift applicable layer are moved to the phase-shift-patternoutput layer, the compaction is executed by the compactor providing thedesign rule about the phase-shift applicable layer and thephase-shift-pattern output layer. This design rule includes the designrule S2 between patterns included in the same layer, and the design ruleS1 between the pattern included in the phase-shift applicable layer andthat included in the phase-shift-pattern output layer.

A spacing between patterns in specific locations may be designated asconstraints for the compactor. For this purpose, the circuit designermay provide a specific-valued design rule which is to be applied inbetween the patterns in those specific, locations, and which differsfrom that of S1 and S2.

As a result of having executed the compaction, there will beautomatically generated the mask layout which is designed by the designrule S2 for use with patterns having the same phase, and the design ruleS1 for patterns having the opposite phase. Thereafter, in order to formmask drawing data, a logical sum (OR) of the phase-shift applicablelayer and the phase-shift-pattern output layer is taken so as to befirst mask drawing data. Then, either of the phase-shift-pattern outputlayer or the phase-shift applicable layer is chosen, so that then chosenlayer is re-sized if necessary and can serve as second mask drawingdata.

FIG. 12 shows the preferable structure of apparatus for performingautomatic phase assignment which comprises:

(1) an input portion where the circuit designer controls the processingof the apparatus;

(2) a first compaction means which executes the compaction by the designrule that is an arbitrary value, about the phase-shift applied layer inthe symbolic layout data;

(3) a phase assigning means which determines the phase (0° or 180° ) ofnet (composed of electrically equivalent elements) in the thephase-shift applicable layer which is compaction-executed in the above(2);

(4) a second compaction means which executes again the compaction in amanner that the spacing between a pair of nets having the same phase isgiven the design rule S2,,and the spacing between a pair of nets havingthe opposite phases is given the design rule S1, based on the resultobtained from the phase assigning means (3), where S1<S2;

(5) a pattern data storing portion which interacts with a controlportion composed of the first compaction means, the phase assigningmeans and the second compaction means; and

(6) a display means which displays the result of phase shifterarrangement and which is connected to the control portion.

In summary, by implementing the method and apparatus for designing thephotomask according to the present invention, once the layout iscompleted, the phase shifters are automatically arranged, so that afinal layout that is maximally compacted can be formed, thussignificantly improving designing efficiency. Moreover, the presentinvention can be applied to optimally designing Application-SpecificIntegrated Circuits (ASIC) where oftentimes the layout is formedautomatically by a CAD software. That is to say, according to thepresent invention, the Levenson-type phase shift masks can be applied tobroader fields of products.

Moreover, the optimum arrangement is selected even in the event thatthere exist plural candidates of phase shifter arrangements, so thatminimum-area-occupying mask layout can be obtained.

Moreover, the symbolic layout data can have phase information therein,so that the Levenson-type phase shift masks can be applied to wide rangeof products.

Besides those already mentioned above, many modifications and variationsof the above embodiments may be made without departing from the noveland advantageous features of the present invention. Accordingly, allsuch modifications and variations are intended to be included within thescope of the appended claims.

What is claimed is:
 1. A method for designing a mask having at least afirst, a second and a third transmissive area, a first light shieldingarea between the first and the second transmissive areas, and a secondlight shielding area between the second and the third transmissive areasin a manner that a phase shifter of the mask is arranged on one of thefirst, second and third transmissive areas so that a phase differencebetween the transmissive area on which the phase shifter is arranged andthe other transmissive areas is set to 180°, the method comprising thesteps of:forming symbolic layout data in which a spacing between theadjacent transmissive areas is set to an arbitrary value, the symboliclayout data corresponding to dimensionless layout data in which onlyrelative positions between symbols are specified; determining regionshaving a mutual phase difference 0° or 180° of light transmittingthrough the adjacent transmissive areas in the symbolic layout data;executing compaction of the symbolic layout, data based on a firstsymbolic layout, in a manner that a minimum spacing between transmissiveareas neighboring with the phase difference of 180° is S1 and a minimumspacing between the transmissive areas neighboring with the phasedifference of 0° is S2; and forming mask layout data such that S1 isless than S2.
 2. The method of claim 1, wherein the region determiningstep includes:assigning phases by giving priority of assigning oppositephases so that the priority is given to a pair of patterns whose lengthof sides thereof facing less than a predetermined threshold is greaterthan other pair of patterns.
 3. The method of claim 1, wherein theregion determining step includes:expressing neighboring relation by agraph represented by a loop and a weighting factor so that the weightingof sides for the graph is determined optimally, the weighting factorincluding:(1) heavier weighting is given for greater minimum distancebetween the patterns; (2) heavier weighting is given for a shorter sideof patterns facing each other within a predetermined threshold; (3)heavier weighting is given to a side of the graph included in greaternumber of closed loops; and (4) heavier weighting is given for patternregions having less area within the threshold.
 4. A method for designinga mask having at least a first and a second nets, each net having acontinuous transmissive area composed of electrically equivalentelements and a light shielding area between the first and second netswhere a phase shifter giving a phase difference to incident raytransmitting through the transmissive areas is arranged on a specifictransmissive area, the method comprising the steps of:forming symboliclayout data, the symbolic layout data corresponding to dimensionlesslayout data in which only relative positions between symbols arespecified; executing first compaction on a phase-shift applicable layerin a manner that a minimum spacing between the transmissive areas is S3that is an arbitrary value; assigning a phase difference in the firstand second nets to either 0° or 180°; executing second compaction, basedon the phase assigning step, in a manner that a minimum spacing of S2 isadopted for the net having the phase difference of 0° assigned, and aminimum spacing of S1 is adopted for the net having the phase differenceof 180° assigned, where the minimum spacing S1 is less than S2; andforming mask data based on the second compaction execution.
 5. Themethod of claim 4, wherein the step of assigning the phase difference inthe first and the second nets to either 0° or 180° includes the stepsof:measuring a minimum spacing between patterns existing in the layoutwhich was compaction-executed by the first compaction; memorizing arelation of patterns that a pair of patterns whose minimum spacingtherebetween is S3, is adjacent to each other; and assigning a phase,based on the memorized adjacent relation of patterns in the memorizingstep, in a manner that tracing back the memorized relation of patterns,opposite phases are assigned to patterns that are adjacent to eachother.
 6. The method of claim 4, wherein the step of assigning the phasedifference in the first and second nets to either 0° or 180°includes:executing again compaction such that a minimum spacing betweenthe transmissive areas in each net is S2 when the phase differencebetween the nets is 0° while the minimum spacing is S1 when the phasedifference between the nets is 180°, so as to form mask data, in theevent that there exist plural types of determining results, where S1 isless than S2; and selecting mask data by which a mask area therefor isminimum by comparing the mask area thus formed.
 7. The method of claim4, wherein the phase assigning step includes:assigning phases by givingpriorty of assigning opposites phases so that the priority is given to apair of patterns whose length of sides thereof facing less than apredetermined threshold is greater than other pair of patterns.
 8. Themethod of claim 7, wherein the phase assigning step includes:expressingneighboring relation by a graph represented by a loop and a weightingfactor so that the weighting of sides for the graph is determinedoptimally, the weighting factor including:(1) heavier weighting is givenfor greater minimum distance between the patterns; (2) heavier weightingis given for a shorter side of patterns facing each other within apredetermined threshold; (3) heavier weighting is given to a side of thegraph included in greater number of closed loops; and (4) heavierweighting is given for pattern regions having less area within thethreshold.
 9. A method for designing a set of mask layers, at least oneof the mask layers is a phase-shift applied layer, the phase-shiftapplied layer is formed in a manner that a phase shifter of the mask isarranged so that a phase difference between light transmitted throughfirst transmissive areas with the phase shifter and the lighttransmitted through second transmissive areas without the phase shifteris set to 180° the phase-shift applied layer having a light shieldingarea between the first and the second transmissive areas arrangedadjacent to the first transmissive areas, the method comprising thesteps of:forming first symbolic layout data, the first symbolic layoutdata corresponding to dimensionless layout data in which only relativepositions between symbols are specified; executing first compaction on aphase-shift applied layer by a design rule that has an arbitrary valueof minimum spacing; determining regions having a mutual phase differenceof 0° or 180° of light transmitting through the adjacent first andsecond transmissive areas in the first symbolic layout data; formingmore than two and less than 2^(n) (inclusive) types of derivativesymbols for each type of symbols by combination of the phase-shiftapplied layer and a phase-shift-pattern output layer thereof, in theevent that an element constituting the symbolic layout includes nphase-shift applied layers where n indicates a positive integer; formingsecond symbolic layout data whose symbols were replaced by theirderivative symbols according to the result of the determination of phasedifference; executing second compaction of the second symbolic layoutdata, in a manner that a design rule S1 having a minimum spacing of S1is adopted to the transmissive areas neighboring with the phasedifference of 180° and a design rule S2 having a minimum spacing of S2is adopted to the transmissive areas neighboring with the phasedifference of 0°; and forming mask layout data such that S1 is less thanS2.
 10. The method of claim 9, wherein the first symbolic layout dataincludes a circuit element which is provided to have electrical contactbetween a first mask layer and a second mask layer, and wherein when thephase shifter is applied simultaneously to both the first and secondmask layers or n being two, there are formed three derivative symbols ofcontacts between the phase-shift-pattern output layer of the first masklayer and that of the second mask layer, in addition to originallyexisting contact of between the first and second mask layers, with atotal of four contacts.
 11. The method of claim 9, wherein the regiondetermining step includes:assigning phases by giving priority ofassigning opposites phases so that the priority is given to a pair ofpatterns whose length of sides thereof facing less than a predeterminedthreshold is greater than other pair of patterns.
 12. The method ofclaim 11, wherein the region determining step includes:expressingneighboring relation by a graph represented by a loop and a weightingfactor so that the weighting of sides for the graph is determinedoptimally, the weighting factor including:(1) heavier weighting is givenfor greater minimum distance between the patterns; (2) heavier weightingis given for a shorter side of patterns facing each other within apredetermined threshold; (3) heavier weighting is given to a side of thegraph included in greater number of closed loops; and (4) heavierweighting is given for pattern regions having less area within thethreshold.
 13. A method for designing a mask having at least a first, asecond and a third transmissive areas, a first light shielding areabetween the first and the second transmissive areas, and a second lightshielding area between the second and the third transmissive areas in amanner that phase shifters of the mask are arranged on two oftransmissive areas among the first, second and third transmissive areasso that a phase difference between the transmissive areas on which thephase shifter is arranged and is not arranged is set to 180°, the methodcomprising the steps of:forming symbolic layout data in which a spacingbetween the adjacent transmissive areas is set to an arbitrary value,the symbolic layout data corresponding to dimensionless layout data inwhich only relative positions between symbols are specified; determiningregions having a mutual phase difference 0° or 180° of lighttransmitting through the adjacent transmissive areas in the symboliclayout data; executing compaction of the symbolic layout data, in amanner such that a minimum spacing between the transmissive areasneighboring with the phase difference of 180° is S1 and a minimumspacing between the transmissive areas neighboring with the phasedifference of 0° is S2; and forming mask layout data such that S1 isless than S2.